The terms alpha and beta have always been pretty arbitrary, I don't care what wikipedia tells you.
When using iterative and incremental development methods (and who isn't nowadays?), the oft cited technical definitions become essentially bloody meaningless. They're just marketing terms as much as anything now.
This is what I used to tell people. Having run a software company greek letters in software development is whatever legal will let marketing/sales get away with. At my company it went like this:
Sales Guy: "We have a big trade show coming up next month. We need a new 'Beta' product to show them and get them interested in sales..." (mind you it was avg 95 days from point of first contact until sales contract inked for our business)
Engineering: "We don't have a 'beta' product. Current development build (insert long laundry list of missing/broken stuff)...we might have an 'Alpha'"
Sales Guy: "If I show them something called Alpha they won't be interested in the product until next year. That's what 'Alpha' means to our customers, it might be ready next year. Beta means it will be ready this year."
Engineering: "That's not what those words..."
Sales Guy: "Business people make the purchasing decisions not geeks. They don't give a damn what you think they mean I only give a damn what they think it means. And Alpha to them means they'll take a look again next year or will go with a competing product."
Me: "Sales guy has a point".
Legal: "Alpha/Beta could have meaning that would imply a state of readiness and some customers might find misleading if we end up with a delay"
Me: "Good point Ms. Lawyer lady...hmmm. What if we called it something else. Like version X 'preview'?"
Sales Guy: "Preview...I like it. I can sell that to people and whet their appitites for the final version."
Engineering: "I guess. I mean it still won't have (laundry list)."
Sales Guy: "So long as you have one or two new features that's fine. We'll only show it on stage or in a presentation. Let others play with the existing product on the floor".
Me: "All right, then have Version X preview release ready next month engineering."